Answer :
Step 1: Identify the forces acting on the wagon. Two horses are pulling the wagon with forces of
[tex]$$ F_1 = 193 \, \text{N} $$[/tex]
and
[tex]$$ F_2 = 207 \, \text{N}. $$[/tex]
Step 2: Calculate the total force exerted on the wagon by adding the two forces:
[tex]$$ F_{\text{total}} = F_1 + F_2 = 193 \, \text{N} + 207 \, \text{N} = 400 \, \text{N}. $$[/tex]
Step 3: Use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
[tex]$$ F = m \cdot a. $$[/tex]
Step 4: Solve for the acceleration [tex]$a$[/tex] by rearranging the formula:
[tex]$$ a = \frac{F_{\text{total}}}{m}. $$[/tex]
Step 5: Substitute the total force and the mass of the wagon (412 kg) into the equation:
[tex]$$ a = \frac{400 \, \text{N}}{412 \, \text{kg}}. $$[/tex]
Step 6: Calculate the acceleration:
[tex]$$ a \approx 0.970873786407767 \, \text{m/s}^2. $$[/tex]
Thus, the acceleration of the wagon is approximately
[tex]$$ 0.97 \, \text{m/s}^2. $$[/tex]
[tex]$$ F_1 = 193 \, \text{N} $$[/tex]
and
[tex]$$ F_2 = 207 \, \text{N}. $$[/tex]
Step 2: Calculate the total force exerted on the wagon by adding the two forces:
[tex]$$ F_{\text{total}} = F_1 + F_2 = 193 \, \text{N} + 207 \, \text{N} = 400 \, \text{N}. $$[/tex]
Step 3: Use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
[tex]$$ F = m \cdot a. $$[/tex]
Step 4: Solve for the acceleration [tex]$a$[/tex] by rearranging the formula:
[tex]$$ a = \frac{F_{\text{total}}}{m}. $$[/tex]
Step 5: Substitute the total force and the mass of the wagon (412 kg) into the equation:
[tex]$$ a = \frac{400 \, \text{N}}{412 \, \text{kg}}. $$[/tex]
Step 6: Calculate the acceleration:
[tex]$$ a \approx 0.970873786407767 \, \text{m/s}^2. $$[/tex]
Thus, the acceleration of the wagon is approximately
[tex]$$ 0.97 \, \text{m/s}^2. $$[/tex]
